We propose a unified model of syntax and discourse in which text structure is viewed as a tree structure augmented with anaphoric relations and other secondary relations. We describe how the model accounts for discourse connectives and the syntax-discourse-semantics interface. Our model is dependency-based, ie, words are the basic building blocks in our analyses. The analyses have been applied cross-linguistically in the Copenhagen Dependency Treebanks, a set of parallel treebanks for Danish, English, German, Italian, and Spanish which are currently being annotated with respect to discourse, anaphora, syntax, morphology, and translational equivalence.